A FEW QUESTIONS IN HYDRODYNAMICS. 
97 
in partially enclosed areas having for free period the period 
of the tidal forces very nearly. We can begin by consider¬ 
ing, on a small scale, an oscillation existing between two 
opposing parallel walls or barriers placed in water of uniform 
depth. The barriers may consist of two thin boards. Their 
lengths may be equal or unequal; they may stand alone 
totally surrounded by water, or they may be backed by solid 
material; they may contain openings ; they may not be high 
enough to reach to the surface of the water: each variation 
of the conditions presents a somewhat different problem. 
Again, lateral boundaries possessing varying degrees of com¬ 
pleteness may be erected. A fairly satisfactory answer to any 
of these questions will be an important contribution to the 
science of hydrodynamics. A somewhat analogous subject is 
that of the vibration of a stretched membrane, where a por¬ 
tion of the rigid boundary is wanting; but the analogy is 
obviously incomplete, because we are in this latter case con¬ 
cerned only with the membrane itself. The problem of an 
open organ pipe is in some respects more nearly analogous 
to the one in question; for, account must be taken of the mo¬ 
tion of the air outside of the pipe as well as of the air within. 
Again, the motion is different according as the pipe is or is 
not provided with a plane flange extending outward indefi¬ 
nitely from the open end. These two cases seem to be some¬ 
what analogous to cases already mentioned, viz., where the 
walls are or are not backed by solid material. The motion 
in an open organ pipe has been investigated by D. Bernoulli, 
Euler, and Lagrange, but more thoroughly by Helmholtz and 
Rayleigh. When the diameter of the pipe is a considerable 
fraction of its length, the problem becomes very difficult. 
Perhaps this possesses further analogies to the question under 
consideration because the motion set up by the plane walls, 
3 
say -j- A in length, is much different from the motion due to 
walls, say -i A in length A being their distance apart ^, 
although the periodic times are but slightly affected by vary¬ 
ing the lengths of the walls. Resonators more or less effective 
